Convection studies of temperature‐dependent Newtonian and non‐Newtonian rheology in aspect‐ratio seven boxes have been carried out for volume averaged Rayleigh numbers between O(105) and O(107). Large lateral viscosity variations, O(104) are found for non‐Newtonian cases with total temperature‐dependent viscosity variations up to 250. Flow structures for both rheologies are distinguished by large‐scale circulations with relatively stable descending limbs. Much larger hot thermal anomalies are found near the surface for non‐Newtonian rheology. Lithospheric thinning is facilitated by non‐Newtonian rheology because of stress‐softening and the lubrication of the descending limbs by hot diapirs.